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How do you simplify #sin^2x csc^2x - sin^2x#?

1 Answer

KillerBunny · Aldrich

Sep 3, 2015

The expression simplifies into #cos^2(x)#

Explanation:

You only need to write down the definitions: since #csc(x)=1/{\sin(x)}#, we have that

#\sin^2(x) * csc^2(x) - \sin^2(x) = {\sin^2(x)}/{\sin^2(x)} - \sin^2(x)#

The first term is obviously #1#, so you have #1-\sin^2(x)#, which equals #\cos^2(x)# because of the fundamental formula #\cos^2(x)+\sin^2(x)=1#

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